Formation of self-sustained states localized in space, so-called localised activity bumps, is a frequent phenomenon in biological neural networks [1]}. In particular, such states have been reported by neurophysiologists and associated with such brain functions as working memory [2]}, [3]} and head-direction control [4]}, [5]}. A broad spectrum of mathematical models is used for the investigation of such structures in different forms: stationary soliton solution [6]}, [7]}, localised oscillating structures [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, propagating and expanding patterns [14]}. In the present work, the existence and expansion of spiking activity bumps in ensembles of bistable oscillators are explored. Here, the property of bistability in the studied models results from the coexistence of a stable limit cycle and a stable steady state in the phase space of an individual (uncoupled) oscillator.
